In the US law, they're referred to as limitations, defenses, and exceptions.

Creative Commons licenses do not affect exceptions and limitations to copyright laws as this was already taken into account when the Creative Commons license was drafter. You can find more information from the Creative Commons section of the Wikipedia website.

Nothing. Copyright law includes a huge number of limitations, defenses, and exceptions, many of which allow certain unlicensed educational uses.

Without the many limitations, defenses, and exceptions included in copyright law, it would prevent reasonable educational uses, commentary, and most importantly free speech.

It's not strictly a paradox; fair use is a clause in the copyright law allowing certain limited unlicensed uses. It is only one of many limitations, defenses, and exceptions to the exclusive rights of the copyright holder.